In this section we formulate an RBM instance entirely in terms of its corresponding weight matrix, and express the action of a spin flip as vertex switching [1]}, which is defined as the negation of the signs of a certain subset of weight elements. We then introduce a measure of the hardness of an RBM instance known as the frustration index [2]}, [3]} and discuss its relationship to the population of local minima of the RBM instance. For simplicity, we assume from here on that the RBM is unbiased [4]} (unless specifically mentioned), meaning that we can set \(\mathbf {a}=0\)  and \(\mathbf {b}=0\) . Note that most of the results derived in this paper can be easily generalized to a biased RBM.
